Noncompactness principles in nonlinear operator approximation theory

Jürgen Appell and Maria Patrizia Pera

Vol. 115 (1984), No. 1, 13–31

DOI: 10.2140/pjm.1984.115.13

Abstract

This paper, which builds on recent work of Anselone and Ansorge, is concerned with the approximate solution of nonlinear equations involving noncompact operators. Roughly speaking, the concepts developed (such as “measure of d-noncompactness”, “generalized noncompact convergence”, etc.) play the same role for approximation problems as the theory of condensing operators for existence problems.

Milestones

Received: 28 January 1983

Published: 1 November 1984